Subgroup posets, Bredon cohomology and equivariant Euler characteristics
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- by Conchita Martínez-Pérez PDF
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Abstract:
For discrete groups $\Gamma$ with a bound on the order of their finite subgroups, we construct Bredon projective resolutions of the trivial module in terms of projective covers of the chain complex associated to the poset of finite subgroups. We use this to give new results on dimensions of $\underline {\operatorname {E}}\Gamma$ and to reprove that for virtually solvable groups, $\underline {\mathrm {cd}}\Gamma =\mathrm {vcd}\Gamma$. We also deduce a formula to compute the equivariant Euler class of $\underline {\operatorname {E}}\Gamma$ for $\Gamma$ virtually solvable of type $\mathrm {FP}_\infty$ and use it to compute orbifold Euler characteristics.References
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Additional Information
- Conchita Martínez-Pérez
- Affiliation: Departamento de Matemáticas, IUMA. Universidad de Zaragoza, 50009 Zaragoza, Spain
- Email: conmar@unizar.es
- Received by editor(s): October 17, 2011
- Received by editor(s) in revised form: December 19, 2011
- Published electronically: February 7, 2013
- Additional Notes: The author was partially supported by BFM2010-19938-C03-03, Gobierno de Aragón and the European Union’s ERDF funds
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 4351-4370
- MSC (2010): Primary 20J05, 18G35, 18G30, 20J06
- DOI: https://doi.org/10.1090/S0002-9947-2013-05781-9
- MathSciNet review: 3055698